Pricing of barrier options by marginal functional quantization

TL;DR

This paper introduces a novel quadratic quantization method for pricing barrier options, providing an alternative to traditional techniques with demonstrated numerical effectiveness in different models.

Contribution

It develops a new optimal quadratic functional quantization approach for barrier option pricing, offering a different computational algorithm compared to existing methods.

Findings

Effective pricing in Black-Scholes and local volatility models

Comparable accuracy to Brownian Bridge method

Numerical tests validate the proposed approach

Abstract

This paper is devoted to the pricing of Barrier options by optimal quadratic quantization method. From a known useful representation of the premium of barrier options one deduces an algorithm similar to one used to estimate nonlinear filter using quadratic optimal functional quantization. Some numerical tests are fulfilled in the Black-Scholes model and in a local volatility model and a comparison to the so called Brownian Bridge method is also done.